Minenhle registers vehicles for the Department of Transportation. Leased vehicles make up $6\%$ of the vehicles she registers. Let $V$ be the number of vehicles Minenhle registers in a day until she first registers a leased vehicle. Assume the status of each vehicle is independent. Find the probability that Minenhle registers a leased vehicle within the first $3$ vehicles of the day. You may round your answer to the nearest hundredth. $P(V \leq 3)=$
Without a fancy calculator For each vehicle: $P({\text{leased}})=0.06$ $P(\text{not}})=0.94$ If Minenhle first registers a leased vehicle in the first $3$ vehicles of the day, here are the possible sequences of vehicles: leased not, leased not, not, leased We can find the probability of each sequence and add those probabilities together. $\begin{aligned} P({\text{leased}}) &= {0.06}\\\\\\ P(\text{not}},{\text{leased}}) &= (0.94})({0.06})\\\\&=0.0564\\\\\\ P(\text{not}},\text{not}},{\text{leased}}) &= (0.94})^2({0.06})\\\\&=0.053016\\\\\\ P(V\leq 3) &= 0.06+0.0564+0.053016 \\\\&=0.169416 \end{aligned}$ [Is there another way?] $P(V \leq 3) \approx 0.17$